Numerous dismutation and transalkylation catalysts based on mordenite have been described in the prior art. The mordenite used has a monodimensional microporous network with a pore diameter of 7.times.6.5.ANG. (1.ANG.=1 Angstrom=1.times.10.sup.-10 m) ("Atlas of Zeolite Structure Types", W. M. Meier and D. H. Olson, 3.sup.rd edition, 1992). This is the case in United States patent U.S. Pat. No. 3,506,731 where a mordenite in its hydrogen form is used and in French patent application FR-A-2 367 533. This is also the case in U.S. Pat. No. 3,281,483 which mentions mordenites which are exchanged essentially with silver or nickel ions, or in U.S. Pat. No. 3,780,121 which describes a mordenite exchanged with metals from group IB of the periodic classification of the elements and which is characterized by a Si/Al atomic ratio which is in the range 6 to 40; U.S. Pat. No. 3,629,351 also concerns a mordenite containing ions of metals from groups IB, VA, VIA, IIA and VIII of the periodic classification of the elements.
More recently, U.S. Pat. No. 5,210,356 has claimed the use of a toluene dismutation catalyst which comprises an omega zeolite which has been modified by dealuminization and charged with nickel.
U.S. Pat. No. 5,371,311 teaches that a catalyst comprising an omega zeolite synthesised using alkaline cations and an organic agent as an organic structuring agent, then modified by calcining in air, ion exchanges, calcining in the presence of steam and finally by treatment with an aqueous solution of ammonium ions at low pH, results in superior physico-chemical properties and improved catalytic performances in hydrocarbon conversion reactions, in particular dismutation and/or transalkylation of alkylaromatics.